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Fast Algorithms for Surface Reconstruction from Point Cloud

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Mathematical Methods in Image Processing and Inverse Problems (IPIP 2018)

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Abstract

We consider constructing a surface from a given set of point cloud data. We explore two fast algorithms to minimize the weighted minimum surface energy in [Zhao, Osher, Merriman and Kang, Comp Vision and Image Under, 80(3):295–319, 2000]. An approach using Semi-Implicit Method (SIM) improves the computational efficiency through relaxation on the time-step constraint. An approach based on Augmented Lagrangian Method (ALM) reduces the run-time via an Alternating Direction Method of Multipliers-type algorithm, where each sub-problem is solved efficiently. We analyze the effects of the parameters on the level-set evolution and explore the connection between these two approaches. We present numerical examples to validate our algorithms in terms of their accuracy and efficiency.

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Author information

Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Mathematics, Atlanta, USA

    Yuchen He, Sung Ha Kang & Hao Liu

  2. Department of Mathematics, University of Bologna, Bologna, Italy

    Martin Huska

Authors
  1. Yuchen He
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  2. Martin Huska
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  3. Sung Ha Kang
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  4. Hao Liu
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Corresponding author

Correspondence to Sung Ha Kang .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong

    Xue-Cheng Tai

  2. Institute of Applied Physics and Computational Mathematics, Beijing, China

    Suhua Wei

  3. Beijing Computational Science Research Center, Beijing, China

    Haiguang Liu

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He, Y., Huska, M., Kang, S.H., Liu, H. (2021). Fast Algorithms for Surface Reconstruction from Point Cloud. In: Tai, XC., Wei, S., Liu, H. (eds) Mathematical Methods in Image Processing and Inverse Problems. IPIP 2018. Springer Proceedings in Mathematics & Statistics, vol 360. Springer, Singapore. https://doi.org/10.1007/978-981-16-2701-9_4

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